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Using curvature and torsion to describe Lagrangian trajectories gives a fulldescription of these as well as an insight into small and large time scales astemporal derivatives up to order 3 are involved. One might expect that thestatistics of these properties depend on the geometry of the flow. Therefore,we calculated curvature and torsion probability density functions (PDFs) ofexperimental Lagrangian trajectories processed using the Shake-the-Boxalgorithm of turbulent von K\'arm\'an flow, Rayleigh-B\'enard convection and azero-pressure-gradient turbulent boundary layer over a flat plate. The resultsfor the von K\'arm\'an flow compare well with previous experimental results forthe curvature PDF and numerical simulation of homogeneous and isotropicturbulence for the torsion PDF. Results for Rayleigh-B\'enard convection agreewith those obtained for K\'arm\'an flow, while results for the logarithmiclayer within the boundary layer differ slightly, and we provide a potentialexplanation. To detect and quantify the effect of anisotropy either resultingfrom a mean flow or large-scale coherent motions on the geometry or tracerparticle trajectories, we introduce the curvature vector. We connect itsstatistics with those of velocity fluctuations and demonstrate that stronglarge-scale motion in a given spatial direction results in meandering ratherthan helical trajectories.

Effects of anisotropy on the geometry of tracer particle trajectories in turbulent flows